Forward Modeling of Magnetic Field Measurements at the Bases of Stellar Coronae through Extreme-ultraviolet Spectroscopy

Abstract

Measurements of the stellar coronal magnetic field are of great importance for understanding stellar magnetic activity, yet such measurements have been extremely difficult to obtain. Recent studies proposed a new method of obtaining magnetic field measurements based on the magnetic-field-induced transition (MIT) of the Fe x ion. Here we construct a series of stellar coronal magnetohydrodynamics models and synthesize several Fe x emission lines at extreme-ultraviolet wavelengths, and then diagnose the magnetic field strength at the bases of the coronae using the MIT technique. Our results show that the technique can be applied to some stars with magnetic fields more than three times higher than that of the Sun at solar maximum. Furthermore, we investigate the uncertainty of the derived magnetic field strength caused by photon counting errors and find that a signal-noise ratio of ∼50 for the Fe x 175 Å line is required to achieve effective measurements of the stellar coronal magnetic field.

Application of a Magnetic-field-induced Transition in Fe x to Solar and Stellar Coronal Magnetic Field Measurements

“…The MIT method can be used to diagnose the magnetic field strength of stars with a magnetic flux density of at least 3 times higher than that of the Sun at the solar maximum, and the differences between the MITmeasured field strengths and the values in the models are less than a factor of 2. It is worth noting that the average coronal temperatures in the stellar models of Chen et al (2021c) and Liu et al (2022) reach up to 10 6.5 K. Considering that the contribution functions of the Fe X lines peak at 10 6.0 K, these Fe X emissions are mainly from the base of stellar coronae. Thus, according to the forward modeling of Chen et al (2021bChen et al ( , 2021c and Liu et al (2022), the MIT method has the potential to measure the magnetic field strength at the coronal bases of some nearby stars with a mean surface magnetic flux density a few times higher than that of the Sun.…”

“…It is worth noting that the average coronal temperatures in the stellar models of Chen et al (2021c) and Liu et al (2022) reach up to 10 6.5 K. Considering that the contribution functions of the Fe X lines peak at 10 6.0 K, these Fe X emissions are mainly from the base of stellar coronae. Thus, according to the forward modeling of Chen et al (2021bChen et al ( , 2021c and Liu et al (2022), the MIT method has the potential to measure the magnetic field strength at the coronal bases of some nearby stars with a mean surface magnetic flux density a few times higher than that of the Sun.…”

“…In Chen et al (2021c), the input photospheric magnetograms of the MHD models were scaled from a solar photospheric magnetogram taken during a relatively inactive phase of the solar cycle, which may not be appropriate for investigations of magnetic fields on active stars or solar-type stars at the peak of their long-term activity cycles (Wilson 1978). More recently, Liu et al (2022) constructed a series of stellar MHD models, in which the photospheric magnetograms are scaled from a solar synchronous magnetogram taken during the solar maximum. They applied the MIT technique in Chen et al (2021c) and the results are featured in Figure 9.…”

“…It has since been applied to the spectral observations taken by the EUV Imaging Spectrometer (EIS, Culhane et al 2007) onboard Hinode (Kosugi et al 2007) for the measurements of coronal magnetic fields in active regions at the limb and on the disk (Landi et al 2020a;Si et al 2020;Brooks & Yardley 2021). Based on forward modeling with 3D MHD models of solar and stellar coronae, Chen et al (2021bChen et al ( , 2021c and Liu et al (2022) demonstrated that the MIT method could provide coronal magnetic field measurements in solar active regions and Sunlike stars with a strong surface magnetic flux.…”

Solar coronal magnetic field measurements using spectral lines available in Hinode/EIS observations: Strong and weak field techniques and temperature diagnostics

“…Recently, Li et al (2015Li et al ( , 2016 noticed the magnetic-field-induced transition (MIT) in the Fe ion and suggested that it can be used to diagnose coronal magnetic field strength (also see Li et al 2021;Xu et al 2022). Si et al (2020) developed the direct line ratio technique and applied this method to spectral observations taken by EUV Imaging Spectrometer (EIS, Culhane et al 2007) onboard Hinode, and the suitability of the method has been validated through forward modeling with a series of MHD models (Chen et al 2021a(Chen et al ,b, 2023Liu et al 2022;Martínez-Sykora et al 2022). Landi et al (2020) further developed the weak and strong magnetic field techniques, which has been applied to EIS observations in flare regions (Landi et al 2021) and coronal loops Brooks & Yardley 2021).…”